Number of the day: 330395165736

Properties of the number 330395165736:

330395165736 = 2³ × 3 × 181 × 293 × 259583 is composite and not squarefree.
330395165736 has 5 distinct prime factors, 64 divisors, 43 antidivisors and 109149039360 totatives.
330395165736 has an emirpimes digit sum 51 in base 10.
Reversing the decimal digits of 330395165736 results in a sphenic number.
330395165736 is the difference of 2 nonnegative squares in 16 ways.
330395165736 is the sum of 2 positive triangular numbers.
330395165736 is the difference of 2 positive pentagonal numbers in 3 ways.
330395165736 = 194² + 6616² + 574762² is the sum of 3 positive squares.
330395165736² = 109990508760² + 311549439936² = 34682365464² + 328569778080² = 42519695400² + 327647739264² = 76678741536² + 321374137320² is the sum of 2 positive squares in 4 ways.
330395165736² is the sum of 3 positive squares.
330395165736 is a proper divisor of 1709^1593882 - 1.

Number of the day: 65596

Properties of the number 65596:

65596 = 2² × 23² × 31 is the 59044^th composite number and is not squarefree.
65596 has 3 distinct prime factors, 18 divisors, 21 antidivisors and 30360 totatives.
65596 has an emirp digit sum 31 in base 10.
65596 = 16400² - 16398² = 736² - 690² = 560² - 498² is the difference of 2 nonnegative squares in 3 ways.
65596 is the sum of 2 positive triangular numbers.
65596 is the difference of 2 positive pentagonal numbers in 3 ways.
65596 is not the sum of 3 positive squares.
65596² is the sum of 3 positive squares.
65596 is a proper divisor of 557²² - 1.
65596 = '6559' + '6' is the concatenation of 2 semiprime numbers.
65596 is palindromic in (at least) the following bases: 48, 52, and 56.
65596 in base 46 = V00 and consists of only the digits '0' and 'V'.
65596 in base 48 = SMS and consists of only the digits 'M' and 'S'.
65596 in base 52 = ODO and consists of only the digits 'D' and 'O'.
65596 in base 56 = KpK and consists of only the digits 'K' and 'p'.

The number 65596 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A114359: Let M(n) be the n X n matrix m(i,j)=min(i,j) for 1<=i,j<=n then a(n) is the trace of M(n)^(-7).
A177269: a(n) = 1 + sum{k=1 to n} A177268(k)

Number of the day: 782975

Properties of the number 782975:

782975 = 5² × 31319 is the 720289^th composite number and is not squarefree.
782975 has 2 distinct prime factors, 6 divisors, 21 antidivisors and 626360 totatives.
782975 has a semiprime digit sum 38 in base 10.
Reversing the decimal digits of 782975 results in a prime.
782975 = 391488² - 391487² = 78300² - 78295² = 15672² - 15647² is the difference of 2 nonnegative squares in 3 ways.
782975 is the sum of 2 positive triangular numbers.
782975 is the difference of 2 positive pentagonal numbers in 3 ways.
782975 is not the sum of 3 positive squares.
782975² = 469785² + 626380² = 219233² + 751656² is the sum of 2 positive squares in 2 ways.
782975² is the sum of 3 positive squares.
782975 is a proper divisor of 101²²³⁷ - 1.

Number of the day: 36440

Norbert Wiener was born on this day 123 years ago.

Properties of the number 36440:

36440 = 2³ × 5 × 911 is the 32577^th composite number and is not squarefree.
36440 has 3 distinct prime factors, 16 divisors, 11 antidivisors and 14560 totatives.
36440 has an emirp digit sum 17 in base 10.
36440 = 40² + … + 55² is the sum of at least 2 consecutive positive squares in 1 way.
36440 = 9111² - 9109² = 4557² - 4553² = 1827² - 1817² = 921² - 901² is the difference of 2 nonnegative squares in 4 ways.
36440 is the difference of 2 positive pentagonal numbers in 2 ways.
36440 = 20² + 38² + 186² is the sum of 3 positive squares.
36440² = 21864² + 29152² is the sum of 2 positive squares in 1 way.
36440² is the sum of 3 positive squares.
36440 is a proper divisor of 1823⁴ - 1.
36440 is palindromic in (at least) the following bases: 43, 66, -69, and -72.
36440 in base 3 = 1211222122 and consists of only the digits '1' and '2'.
36440 in base 19 = 55hh and consists of only the digits '5' and 'h'.
36440 in base 43 = JUJ and consists of only the digits 'J' and 'U'.

Number of the day: 5822

Properties of the number 5822:

5822 = 2 × 41 × 71 is a sphenic number and squarefree.
5822 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 2800 totatives.
5822 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 5822 results in a semiprime.
5822 is the difference of 2 positive pentagonal numbers in 1 way.
5822 = 1² + 14² + 75² is the sum of 3 positive squares.
5822² = 1278² + 5680² is the sum of 2 positive squares in 1 way.
5822² is the sum of 3 positive squares.
5822 is a proper divisor of 857⁵ - 1.
5822 = '58' + '22' is the concatenation of 2 semiprime numbers.
5822 is palindromic in (at least) the following bases: 81, and -60.
5822 in base 3 = 21222122 and consists of only the digits '1' and '2'.
5822 in base 9 = 7878 and consists of only the digits '7' and '8'.
5822 in base 18 = hh8 and consists of only the digits '8' and 'h'.

The number 5822 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000712: Number of partitions of n into parts of 2 kinds.
A048788: a(2n+1) = a(2n) + a(2n-1), a(2n) = 2*a(2n-1) + a(2n-2).
A052530: a(0)=0, a(1)=2; for n>=2, a(n)=4*a(n-1)-a(n-2).
A082630: Start with the sequence S(0)={1,1} and for n > 0 define S(n) to be I(S(n-1)) where I denotes the operation of inserting, for i=1,2,3..., the term a(i) + a(i+1) between any two terms for which 7*a(i+1) <= 11*a(i). The listed terms are the initial terms of the limit of this process.
A097097: Antidiagonal sums of triangle A097094, where self-convolution forms A097096 (row sums of triangle A097094).
A107235: Expansion of 1 / Prod{n>=0} (1-q^(5n+1))(1-q^(5n+2))(1-q^(5n+4)).
A152528: a(n) = p(n)*p(n+2) - 3*p(n+1), where p(n) is the n-th prime.
A208960: T(n,k)=Number of nXk 0..5 arrays with every element value z a city block distance of exactly z from another element value z
A218471: a(n) = n*(7*n-3)/2.
A221255: T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, with no occupancy greater than 2

Number of the day: 11232017

John Wallis was born on this day 401 years ago.

Happy Fibonacci Day!

Properties of the number 11232017:

11232017 is a cyclic number.
11232017 is the 740820^th prime.
11232017 has 13 antidivisors and 11232016 totatives.
11232017 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 11232017 results in a sphenic number.
11232017 = 5616009² - 5616008² is the difference of 2 nonnegative squares in 1 way.
11232017 is the difference of 2 positive pentagonal numbers in 1 way.
11232017 = 1496² + 2999² is the sum of 2 positive squares in 1 way.
11232017 = 55² + 216² + 3344² is the sum of 3 positive squares.
11232017² = 6755985² + 8973008² is the sum of 2 positive squares in 1 way.
11232017² is the sum of 3 positive squares.
11232017 is a proper divisor of 773³⁷⁹⁴⁶ - 1.
11232017 = '1123' + '2017' is the concatenation of 2 prime numbers.
11232017 is an emirp in (at least) the following bases: 2, 7, 24, 31, 37, 38, 47, 50, 55, 62, 63, 75, 76, 79, 80, and 97.

Number of the day: 4371020300

Properties of the number 4371020300:

4371020300 = 2² × 5² × 19 × 401 × 5737 is the 4164311888^th composite number and is not squarefree.
4371020300 has 5 distinct prime factors, 72 divisors, 35 antidivisors and 1651968000 totatives.
4371020300 has an oblong digit sum 20 in base 10.
4371020300 is the difference of 2 nonnegative squares in 12 ways.
4371020300 is the difference of 2 positive pentagonal numbers in 12 ways.
4371020300 = 530² + 858² + 66106² is the sum of 3 positive squares.
4371020300² = 2260722220² + 3740982960² = 1902007920² + 3935503060² = 2599733520² + 3513858860² = 436012000² + 4349219700² = 28528500² + 4370927200² = 839695500² + 4289607200² = 1636353036² + 4053167552² = 1251246976² + 4188102132² = 2007197696² + 3882908172² = 2958341420² + 3217768560² = 2645379120² + 3479624660² = 2927868460² + 3245520720² = 799209996² + 4297334272² = 394982336² + 4353137652² = 1196472256² + 4204078092² = 2622612180² + 3496816240² = 2285090480² + 3726148140² = 2937276880² + 3237008340² = 407616500² + 4351972800² = 1223885684² + 4196179488² = 827240544² + 4292026508² = 1609864224² + 4063761268² is the sum of 2 positive squares in 22 ways.
4371020300² is the sum of 3 positive squares.
4371020300 is a proper divisor of 457⁴⁷⁸⁰ - 1.

Number of the day: 10991

Benoit Mandelbrot was born on this day 93 years ago.

Properties of the number 10991:

10991 is a cyclic number.
10991 = 29 × 379 is semiprime and squarefree.
10991 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 10584 totatives.
10991 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 10991 results in an emirpimes.
10991 = 22³ + 7³ is the sum of 2 positive cubes in 1 way.
10991 = 5496² - 5495² = 204² - 175² is the difference of 2 nonnegative squares in 2 ways.
10991 is the sum of 2 positive triangular numbers.
10991 is the difference of 2 positive pentagonal numbers in 2 ways.
10991 is not the sum of 3 positive squares.
10991² = 7580² + 7959² is the sum of 2 positive squares in 1 way.
10991² is the sum of 3 positive squares.
10991 is a proper divisor of 1567³ - 1.
10991 is an emirpimes in (at least) the following bases: 2, 4, 8, 10, 11, 15, 17, 18, 19, 20, 22, 25, 27, 31, 32, 41, 43, 46, 47, 49, 54, 61, 65, 67, 68, 74, 76, 77, 80, 81, 82, 84, 85, 87, 90, 91, 97, 99, and 100.
10991 is palindromic in (at least) the following bases: 23, 34, -9, -67, and -99.
10991 in base 4 = 2223233 and consists of only the digits '2' and '3'.
10991 in base 23 = khk and consists of only the digits 'h' and 'k'.
10991 in base 27 = f22 and consists of only the digits '2' and 'f'.
10991 in base 34 = 9h9 and consists of only the digits '9' and 'h'.
10991 in base 60 = 33B and consists of only the digits '3' and 'B'.

The number 10991 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A023192: Conjecturally, number of infinitely-recurring prime patterns on n consecutive integers.
A028948: An "extremely strange sequence": a(n+1) = [ A*a(n)+B ]/p^r, where p^r is the highest power of p diving [ A*a(n)+B ] and p=2, A=4.001, B=1.2.
A060354: The n-th n-gonal number.
A066831: Numbers n such that sigma(n) divides sigma(phi(n)).
A067383: Numbers n such that sigma(phi(n))/sigma(n) = 3.
A085366: Semiprimes that are the sum of two positive cubes. Common terms of A003325 and A046315.
A224483: Numbers which are the sum of two positive cubes and divisible by 29.
A252039: T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with every 3X3 subblock row and column sum nonprime and every diagonal and antidiagonal sum prime
A255187: 29-gonal numbers: a(n) = n*(27*n-25)/2.
A262909: a(n) = greatest k such that A155043(k+A262509(n)) < A155043(A262509(n)).

Number of the day: 15987776874

Properties of the number 15987776874:

15987776874 = 2 × 3 × 97 × 27470407 is composite and squarefree.
15987776874 has 4 distinct prime factors, 16 divisors, 13 antidivisors and 5274317952 totatives.
15987776874 has a semiprime digit sum 69 in base 10.
15987776874 = 1192² + 2143² + 126419² is the sum of 3 positive squares.
15987776874² = 10713458730² + 11867215824² is the sum of 2 positive squares in 1 way.
15987776874² is the sum of 3 positive squares.
15987776874 is a proper divisor of 193^9156802 - 1.
15987776874 = '1598' + '7776874' is the concatenation of 2 sphenic numbers.

Number of the day: 879706944

Properties of the number 879706944:

879706944 = 2⁶ × 3² × 23 × 66403 is the 834681825^th composite number and is not squarefree.
879706944 has 4 distinct prime factors, 84 divisors, 31 antidivisors and 280482048 totatives.
879706944 is the difference of 2 nonnegative squares in 30 ways.
879706944 is the sum of 2 positive triangular numbers.
879706944 is the difference of 2 positive pentagonal numbers in 2 ways.
879706944 = 2800² + 4888² + 29120² is the sum of 3 positive squares.
879706944² is the sum of 3 positive squares.
879706944 is a proper divisor of 271⁴⁰⁹² - 1.

Number of the day: 68956

Properties of the number 68956:

68956 = 2² × 17239 is the 62103^th composite number and is not squarefree.
68956 has 2 distinct prime factors, 6 divisors, 3 antidivisors and 34476 totatives.
68956 has a semiprime digit sum 34 in base 10.
68956 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 68956 results in a semiprime.
68956 = 2³ + 3³ + 41³ is the sum of 3 positive cubes in 1 way.
68956 = 17240² - 17238² is the difference of 2 nonnegative squares in 1 way.
68956 is the difference of 2 positive pentagonal numbers in 1 way.
68956 is not the sum of 3 positive squares.
68956² is the sum of 3 positive squares.
68956 is a proper divisor of 509¹⁷ - 1.
68956 in base 51 = QQ4 and consists of only the digits '4' and 'Q'.

The number 68956 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A032375: Numbers n such that 51*2^n+1 is prime.
A184642: Number of partitions of n having no parts with multiplicity 7.

Number of the day: 5471

Properties of the number 5471:

5471 is a cyclic number.
5471 is the 722^th prime.
5471 has 9 antidivisors and 5470 totatives.
5471 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 5471 results in a semiprime.
5471 = 2736² - 2735² is the difference of 2 nonnegative squares in 1 way.
5471 is the difference of 2 positive pentagonal numbers in 1 way.
5471 is not the sum of 3 positive squares.
5471² is the sum of 3 positive squares.
5471 is a proper divisor of 2⁵⁴⁷ - 1.
5471 is an emirp in (at least) the following bases: 3, 5, 7, 9, 11, 13, 14, 16, 19, 20, 32, 33, 41, 49, 51, 55, 56, 57, 59, 61, 62, 64, 65, 66, 68, 69, 74, 77, 81, 83, 85, 86, 87, 91, 93, and 98.
5471 is palindromic in (at least) base -18.
5471 in base 3 = 21111122 and consists of only the digits '1' and '2'.
5471 in base 4 = 1111133 and consists of only the digits '1' and '3'.
5471 in base 20 = ddb and consists of only the digits 'b' and 'd'.

The number 5471 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000945: Euclid-Mullin sequence: a(1) = 2, a(n+1) is smallest prime factor of 1 + Product_{k=1..n} a(k).
A049438: p, p+6 and p+8 are all primes (A046138) but p+2 is not.
A059802: Numbers n such that 5^n - 4^n is prime.
A078853: Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d = 2, 4 or 6) and forming d-pattern=[6,2,4]; short d-string notation of pattern = [624].
A124179: Prime(R(p)) where Prime(i) is the i-th prime and R(p) is the value of the reverse of the digits of prime p.
A136073: Father primes of order 4.
A167054: Values of A167053(k)-A167053(k-1)-1 not equal to 1.
A213978: Number of solid standard Young tableaux of shape [[n,n,n],[n]].
A214722: Number A(n,k) of solid standard Young tableaux of shape [[{n}^k],[n]]; square array A(n,k), n>=0, k>=1, read by antidiagonals.
A250755: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction

Number of the day: 8049637

Properties of the number 8049637:

8049637 is a cyclic number.
8049637 = 73 × 110269 is semiprime and squarefree.
8049637 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 7939296 totatives.
8049637 has an emirp digit sum 37 in base 10.
8049637 = 4024819² - 4024818² = 55171² - 55098² is the difference of 2 nonnegative squares in 2 ways.
8049637 is the sum of 2 positive triangular numbers.
8049637 is the difference of 2 positive pentagonal numbers in 2 ways.
8049637 = 1286² + 2529² = 694² + 2751² is the sum of 2 positive squares in 2 ways.
8049637 = 100² + 231² + 2826² is the sum of 3 positive squares.
8049637² = 5292912² + 6064795² = 4742045² + 6504588² = 3818388² + 7086365² = 1782660² + 7849763² is the sum of 2 positive squares in 4 ways.
8049637² is the sum of 3 positive squares.
8049637 is a proper divisor of 1597³⁰⁶³ - 1.
8049637 is an emirpimes in (at least) the following bases: 3, 5, 12, 13, 14, 15, 16, 17, 20, 21, 29, 31, 38, 41, 44, 49, 51, 55, 60, 61, 62, 71, 78, 83, 88, 93, 94, 95, and 99.

Number of the day: 6674

Properties of the number 6674:

6674 = 2 × 47 × 71 is a sphenic number and squarefree.
6674 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 3220 totatives.
6674 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 6674 results in a semiprime.
6674 is the difference of 2 positive pentagonal numbers in 1 way.
6674 = 7² + 8² + 81² is the sum of 3 positive squares.
6674² is the sum of 3 positive squares.
6674 is a proper divisor of 283² - 1.
6674 = '6' + '674' is the concatenation of 2 semiprime numbers.
6674 is palindromic in (at least) the following bases: 48, 93, -39, and -46.
6674 in base 36 = 55e and consists of only the digits '5' and 'e'.
6674 in base 48 = 2h2 and consists of only the digits '2' and 'h'.

The number 6674 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A137094: Numbers n such that n and the square of n use only the digits 2, 4, 5, 6 and 7.
A137380: Number of primes between (Prime[n + 1])^Pi and (Prime[n])^Pi.
A138563: Beastly fax numbers: numbers containing the fax number of the Beast (667, one more than its regular number) in their decimal expansion.
A186668: Total number of n-digit numbers requiring 11 positive biquadrates in their representation as sum of biquadrates.
A208923: Triangle of coefficients of polynomials u(n,x) jointly generated with A208908; see the Formula section.
A229014: Number of arrays of median of three adjacent elements of some length 6 0..n array, with no adjacent equal elements in the latter.
A252213: Number of (n+2)X(2+2) 0..3 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 0 2 5 6 or 7
A252216: Number of (n+2)X(5+2) 0..3 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 0 2 5 6 or 7
A252219: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 0 2 5 6 or 7
A260370: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00001111

Number of the day: 986633

Properties of the number 986633:

986633 is a cyclic number.
986633 is the 77542^th prime.
986633 has 17 antidivisors and 986632 totatives.
986633 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 986633 results in an emirp.
986633 = 493317² - 493316² is the difference of 2 nonnegative squares in 1 way.
986633 is the difference of 2 positive pentagonal numbers in 1 way.
986633 = 437² + 892² is the sum of 2 positive squares in 1 way.
986633 = 46² + 111² + 986² is the sum of 3 positive squares.
986633² = 604695² + 779608² is the sum of 2 positive squares in 1 way.
986633² is the sum of 3 positive squares.
986633 is a proper divisor of 37⁶⁴⁹¹ - 1.
986633 = '98663' + '3' is the concatenation of 2 prime numbers.
986633 = '9' + '86633' is the concatenation of 2 semiprime numbers.
986633 is an emirp in (at least) the following bases: 9, 10, 15, 21, 42, 49, 52, 59, 64, 71, 79, 83, 88, 89, 91, 92, 98, and 99.
986633 in base 42 = DDDB and consists of only the digits 'B' and 'D'.

Number of the day: 242

Properties of the number 242:

242 = 2 × 11² is the 188^th composite number and is not squarefree.
242 has 2 distinct prime factors, 6 divisors, 10 antidivisors and 110 totatives.
242 has a Fibonacci digit sum 8 in base 10.
242 has sum of divisors equal to 399 which is a sphenic number.
242 = 3⁵ - 1⁵ is the difference of 2 positive fifth powers in 1 way.
242 is the difference of 2 positive pentagonal numbers in 1 way.
242 = 11² + 11² is the sum of 2 positive squares in 1 way.
242 = 1² + 4² + 15² is the sum of 3 positive squares.
242² is the sum of 3 positive squares.
242 is a proper divisor of 241² - 1.
242 = '2' + '42' is the concatenation of 2 oblong numbers.
242 is a palindrome (in base 10).
242 is palindromic in (at least) the following bases: 3, 7, 21, -12, and -15.
242 in base 3 = 22222 and consists of only the digit '2'.
242 in base 7 = 464 and consists of only the digits '4' and '6'.
242 in base 9 = 288 and consists of only the digits '2' and '8'.
242 consists of only the digits '2' and '4'.
242 in base 11 = 200 and consists of only the digits '0' and '2'.
242 in base 15 = 112 and consists of only the digits '1' and '2'.

The number 242 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000982: a(n) = ceiling(n^2/2).
A001105: a(n) = 2*n^2.
A002088: Sum of totient function: a(n) = Sum_{k=1..n} phi(k), cf. A000010.
A002113: Palindromes in base 10.
A002822: Numbers n such that 6n-1, 6n+1 are twin primes.
A008593: Multiples of 11.
A008864: a(n) = prime(n) + 1.
A014612: Numbers that are the product of exactly three (not necessarily distinct) primes.
A028982: Squares and twice squares.
A269303: Numbers n such that (266*10^n+1)/3 is prime.

Number of the day: 59574745

Felix Hausdorff was born on this day 149 years ago.

Properties of the number 59574745:

59574745 is a cyclic number.
59574745 = 5 × 167 × 71347 is a sphenic number and squarefree.
59574745 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 47373744 totatives.
59574745 has a semiprime digit sum 46 in base 10.
59574745 = 29787373² - 29787372² = 5957477² - 5957472² = 178451² - 178284² = 36091² - 35256² is the difference of 2 nonnegative squares in 4 ways.
59574745 is the sum of 2 positive triangular numbers.
59574745 is the difference of 2 positive pentagonal numbers in 4 ways.
59574745 = 315² + 352² + 7704² is the sum of 3 positive squares.
59574745² = 35744847² + 47659796² is the sum of 2 positive squares in 1 way.
59574745² is the sum of 3 positive squares.
59574745 is a proper divisor of 953⁷⁶³⁶ - 1.
59574745 = '5957' + '4745' is the concatenation of 2 sphenic numbers.

Number of the day: 32363

Properties of the number 32363:

32363 is a cyclic number.
32363 is the 3472^th prime.
32363 has 15 antidivisors and 32362 totatives.
32363 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 32363 results in a semiprime.
32363 = 16182² - 16181² is the difference of 2 nonnegative squares in 1 way.
32363 is the difference of 2 positive pentagonal numbers in 1 way.
32363 = 15² + 47² + 173² is the sum of 3 positive squares.
32363² is the sum of 3 positive squares.
32363 is a proper divisor of 349¹⁴⁷¹ - 1.
32363 is an emirp in (at least) the following bases: 11, 14, 19, 29, 31, 32, 34, 37, 52, 54, 59, 63, 66, 67, 74, 76, 77, 79, 83, 94, and 98.
32363 is palindromic in (at least) base -50.
32363 in base 33 = tnn and consists of only the digits 'n' and 't'.
32363 in base 37 = NNP and consists of only the digits 'N' and 'P'.
32363 in base 49 = DNN and consists of only the digits 'D' and 'N'.

The number 32363 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A067921: Engel expansion of sqrt(Pi/2).
A078854: Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d=2,4 or 6) and forming d-pattern=[6, 2,6]; short d-string notation of pattern = [626].
A078959: Primes p such that the differences between the 5 consecutive primes starting with p are (6,2,6,4).
A201851: Primes of the form 7n^2 - 5.
A227282: First primes of arithmetic progressions of 7 primes each with the common difference 210.
A247197: Primes p such that 2*p^2 + 3 and 2*p^2 + 5 are also primes.
A260126: Primes that contain only the digits (2, 3, 6).
A269066: Five-digit primes whose first, third, and fifth digits are the same.
A280937: Expansion of Product_{k>=1} ((1 - x^(7*(2*k-1))) * (1 - x^(7*k)) / (1 - x^k)).

Number of the day: 9162627

Properties of the number 9162627:

9162627 = 3 × 61 × 50069 is a sphenic number and squarefree.
9162627 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 6008160 totatives.
9162627 has a semiprime digit sum 33 in base 10.
9162627 = 4581314² - 4581313² = 1527106² - 1527103² = 75134² - 75073² = 25126² - 24943² is the difference of 2 nonnegative squares in 4 ways.
9162627 is the difference of 2 positive pentagonal numbers in 2 ways.
9162627 = 73² + 137² + 3023² is the sum of 3 positive squares.
9162627² = 6197373² + 6748800² = 1652277² + 9012420² = 3400227² + 8508360² = 4878780² + 7755723² is the sum of 2 positive squares in 4 ways.
9162627² is the sum of 3 positive squares.
9162627 is a proper divisor of 487²⁵⁰³⁴ - 1.

Number of the day: 8054397

Properties of the number 8054397:

8054397 = 3⁴ × 13 × 7649 is the 7511217^th composite number and is not squarefree.
8054397 has 3 distinct prime factors, 20 divisors, 31 antidivisors and 4955904 totatives.
8054397 has a triangular digit sum 36 in base 10.
8054397 is the difference of 2 nonnegative squares in 10 ways.
8054397 is the sum of 2 positive triangular numbers.
8054397 is the difference of 2 positive pentagonal numbers in 2 ways.
8054397 = 846² + 2709² = 261² + 2826² is the sum of 2 positive squares in 2 ways.
8054397 = 116² + 179² + 2830² is the sum of 3 positive squares.
8054397² = 1683747² + 7876440² = 1475172² + 7918155² = 4583628² + 6622965² = 3097845² + 7434828² is the sum of 2 positive squares in 4 ways.
8054397² is the sum of 3 positive squares.
8054397 is a proper divisor of 593²⁸⁶⁸ - 1.

Number of the day: 41310016

Properties of the number 41310016:

41310016 = 2⁶ × 11 × 58679 is the 38801602^th composite number and is not squarefree.
41310016 has 3 distinct prime factors, 28 divisors, 11 antidivisors and 18776960 totatives.
41310016 is the difference of 2 nonnegative squares in 10 ways.
41310016 is the difference of 2 positive pentagonal numbers in 2 ways.
41310016 = 896² + 984² + 6288² is the sum of 3 positive squares.
41310016² is the sum of 3 positive squares.
41310016 is a proper divisor of 353⁵⁸⁶⁷⁸ - 1.

Number of the day: 6915382

George Boole was born on this day 202 years ago.

Properties of the number 6915382:

6915382 = 2 × 661 × 5231 is a sphenic number and squarefree.
6915382 has 3 distinct prime factors, 8 divisors, 33 antidivisors and 3451800 totatives.
6915382 has a semiprime digit sum 34 in base 10.
6915382 has a Fibonacci digit sum 34 in base 10.
6915382 is the difference of 2 positive pentagonal numbers in 3 ways.
6915382 = 42² + 293² + 2613² is the sum of 3 positive squares.
6915382² = 3138600² + 6162118² is the sum of 2 positive squares in 1 way.
6915382² is the sum of 3 positive squares.
6915382 is a proper divisor of 307⁶⁶⁰ - 1.
6915382 = '69' + '15382' is the concatenation of 2 semiprime numbers.

Number of the day: 540484

Properties of the number 540484:

540484 = 2² × 7 × 97 × 199 is the 495875^th composite number and is not squarefree.
540484 has 4 distinct prime factors, 24 divisors, 11 antidivisors and 228096 totatives.
540484 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 540484 results in a sphenic number.
540484 = 135122² - 135120² = 19310² - 19296² = 1490² - 1296² = 878² - 480² is the difference of 2 nonnegative squares in 4 ways.
540484 is the difference of 2 positive pentagonal numbers in 4 ways.
540484 = 72² + 130² + 720² is the sum of 3 positive squares.
540484² = 362180² + 401184² is the sum of 2 positive squares in 1 way.
540484² is the sum of 3 positive squares.
540484 is a proper divisor of 491¹² - 1.